THIS IS AN OLD VERSION OF THE PAGE (OCT. 2001 - JULY 2002.)


*** WELCOME TO FOURIER SERIES & INTEGRAL TRANSFORMS ***
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*** ( F. S. I. T. ) ***
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(The page for earlier semesters, (i.e. for October 2001 and earlier) for Fourier S. I. T. is here.)
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8.7.2002 Some information about the examination on July 12, 2002 is here

We wish you a very pleasant, interesting and successful semester. We realize that the strike will make this considerably harder to achieve. Within the constraints of the situation, we will do whatever we can to minimize the difficulties, and also to help you know what you need for the continuation of your studies next semester.

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I will usually put new information for the course here on my "private" Fourier website.

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INFORMATION about the REDUCED SYLLABUS for this semester is now here. A more detailed version of the syllabus is now here.
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To go to the OFFICIAL website for this course click here. That site also contains ESSENTIAL information, exercises, text book, previous examinations, etc.

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To go directly to download or read the text book for this course, written by Allan Pinkus and Samy Zafrany, click here.
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Information about your lecturers, and how to contact them is here.
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Here is some VERY IMPORTANT information about (1) the format of the tests/exams, (2) homework exercises, (3) the calculation of your tsiyun sofi, (4) miluim during the semester or test or exam, (5) students with learning disabilities or other problems. PLEASE BE SURE TO READ THIS. Not reading it could seriously effect your final grade.
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16.4.02 The solution to Moed bet (14.4.02) is here. One version of the exam itself is here.
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18.3.02 Thanks for waiting. Your grades=marks are on the noticeboard on the 2nd floor of the Amado Building. If you look at the key on the last page you will see that there is a lot of information there, i.e. results for individual questions etc. Sorry it took so long. Congratulations to all who did well, especially those who got 100 or more. (Sorry, your official grades=marks will be "only" 100.) To those who did not do so well, best wishes for improved results soon. As you can see, in general, the results are very good. I take this to mean that most of you took this course seriously. I wish you success in using this information in your future studies and work.
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14.3.02 Some copies of part 2 of the examination are now also available from the same envelope containing part 1, next to my door. You can of course also now get part 2 from this site.
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13.3.02 The solution and examination (27.2.02) now include also Question 3 of part 2. (See below.)
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4.3.02 The solution to the examination (posted below) has now been slightly revised. Something had to be fixed in the solution of question 2 in part 1. Thanks and congratulations to the serious student who first noticed this.
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28.2.02 The (revised) and now COMPLETE solution to yesterday's examination is here. To remember what the questions were yesterday:
1. You can take a hard copy of part one (yellow page) of the exam from one of the two envelopes next to my door. (The other envelope has a different examination. Please leave those pages for the students who need them.)
2. And you can see a "compact" and now COMPLETE version of the two parts of the examination here.
An example of the picture of 6 graphs which appeared as part of the examination is available separately here.
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22.2.02 Here is a 6 page Hebrew document which summarizes some of the basic results about Fourier series.
WARNING: A quick summary can be useful, but it is NOT a substitute for really understanding the material and doing plenty of exercises.
For the examination this semester you only need the results on the first two pages. The remaining four pages give the analogous results when the interval [-pi,pi] is replaced by more general intervals. Thanks to Yoram Yihiye for helping prepare this document.
This document is NOT a list of formulae to be used during the examination. The list of formulae which will appear as part of the examination was posted here on 6/2/02. (See below.)
I have also prepared some other notes. But they are not needed for this semester's examination. They give a proof of the theorem about the inverse Fourier transform, using the same ideas as in the alternative proof of Dirichlet's theorem which was posted here earlier. The simpler version is here and the general version is here.
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6.2.02 A detailed version of the syllabus is now here.
6.2.02 (ctd.) Homework exercise No. 4 has been available from the official course site for quite some time I believe. If you have not yet seen it please go to the official site, and the page of the metargel akhrayey, or use this (temporary) link. But note, as we already told you on 16 Feb, there is a misprint in Question 3 part gimel. The term 2tx(t) in the first equation should be 2tx'(t).
6.2.02 (ctd.) The questionnaire of the examination for Moed Alef, (and similarly for Moed bet,) will include the standard list of formulae that has appeared on most recent exams in this subject. The exact list that we will use is here. It will be provided by US, please do NOT bring your copy. (You will not be allowed to use it.)
If you are looking for old examinations as a source of questions for revision, it should be mentioned that some of these are on the page of the metargel hakhrayi, and some on the main official page of the course. Many are on both sites, but to get absolutely all of them you currently have to visit both of these sites. I will request that both of these sites be updated, to include all examinations, but I do not know when this will be done. (You can also find links to several examinations and bakhanim from my page of last semester.)
6.2.02 (ctd.) Probably you know all or most of what you need to know about partial fractions. (They are sometimes convenient for finding inverse Laplace transforms.) If you want to know about the completely general case you can look here.
If two piecewise continous functions f(x) and g(x) both vanish for all negative x, then their convolution f*g is continuous. Here are the details.
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3.3.02 Here is a REVISED VERSION of a formulation of Fubini's theorem which is useful for changing order of integration in connection with Fourier transforms. (I noticed that one condition was missing in the earlier version. The earlier version is correct if you keep open the option of using Lebesgue integration instead of Riemann integration.)
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21.01.02 Homework exercise no. 3, about Fourier transforms is now available here.
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16.1.02 Here is a formulation (Revised now on 2/2/02) of Fubini's theorem which is useful for changing order of integration in connection with Fourier transforms.
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13.1.02 To find out how to see your bakhan please click here.
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3.1.02 The text of the bakhan of January 1 (in a more compact version) is here. And here is a solution.
I plan to rewrite an improved version of the last part of the notes that I posted here on 26.12.01, i.e. the part about "other intervals". The formulae there are correct, but there is also a simpler version of them.
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29.12.01 Shavua Tov. The second and final part of the solutions/hints for the homework exercises about inner products is here. (English, 6 pages. Please look especially at the first 3 and a half pages. The last two and a half pages are for "freakim".)
In answer to a question from one student: The mid term text is without ANY khomer ezer of any kind.
At this stage there are not so many formulae to remember. If you don't remember them this is perhaps also a sign that you need to do a few more targilim.
(But for the final exam we will almost certainly include the "traditional" two pages of formulae which have been used in the past few years.)
Please remember also that students will not be allowed to leave the room during the test.
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27.12.01 We have decided, after all, to provide solutions for at least some of the homework problems. Here is a solution for Question 2 and part of Question 6 from the first set of homework problems. Maybe there will be additional solutions in the next few days.
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26.12.01. Two announcements:
(1) On December 31, 2001 starting from 16:30 until ?? ... Uri Itai will be available in room 521 Amado to answer questions.
Thank you Uri.
There may perhaps also be other shaot kabala or tirguley hashlama. I will announce any that I am told about.
(2) In my lecture today I forgot to add a constant to a formula for integration term by term of Fourier series. (This topic is NOT for the test on January 1.) For a correction please see here, or read the (now slightly revised)"Term by Term..." notes mentioned on 18.12.01. (Those same notes are also here.)

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24.12.01 Here is some information about the bakhan on January 1.
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19.12.01 The promised summary about uniform convergence is now here.
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18.12.01 You can now get the second set of homework exercises from the official Fourier series website or from here. Maybe some of them will not be relevant for the questions of the midterm test on January 1. We will give exact details later.
In many of the exercises you are asked to determine whether certain Fourier series converge UNIFORMLY (b'mida-shava) on some set. Uniform convergence is a topic which you are supposed to remember from Hedva 1 or Hedva 2. Although in general it is very important, it only plays a limited role in this particular course. Here is a quick summary, a "Uniform Convergence Survival Kit" containing the main things you need to know about Unif.Cgce. for this course.

Here is a summary which I wrote last semester (SLIGHTLY REVISED ON 26.12.01) about two topics: Differentiation and integration of Fourier series, term by term, and Fourier series on other intervals instead of [-pi,pi].
I plan to rewrite an improved version of the last part about "other intervals". The formulae there are correct, but there is also a simpler version of them. REMARKS: (1) This semester, because of the strike, the last topic "other intervals" will be discussed in lectures but not in tirgulim. So we will not ask examination questions about it. (But the second set of homework exercises includes a "targil reshut" about it.) It is not a difficult topic to learn yourselves, and you will need it in other courses, e.g. when you solve differential equations on different intervals. Yoram Yihiye plans to also provide you with a summary in Hebrew of the relevant formulae for Fourier series on different intervals.
(2) There is one very small misprint in these notes which I will try to correct soon. A funny symbol in equation (8) and in some other places should be a zero.

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12.12.01 We will soon be studying the convergence of Fourier series. The main result is Dirichlet's theorem. You DO have to be able to use Dirichlet's theorem and state its result precisely. But this semester, because of the strike, you do NOT have to know how to prove it.
For those who want to know the proof anyway, or at least a simple version of it , there are (at least) three options.
(1) You can study the proof in Chapter 2 of the book by Pinkus and Zafrany.
(2) You can read (3 pages, English) here. This is a short proof of Dirichlet's theorem in a special case where the function f is "nice". There is a fourth page with some further comments and questions.
(3) For a version of the FULL proof which is different from the usual version in (1) you can read 7 pages (English) here. (Part of pages 2 and 3 of this document, is the calculation of the Fourier series of a particular function, which is an exercise that you should be able to do, even if you do not care about the proof of Dirichlet's theorem.)
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10.12.01 PLEASE SEE BELOW FOR UPDATE ABOUT ROOMS FOR EXTRA LECTURES FOR WEDNESDAY.
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10.12.01 Information about the reduced syllabus for this semester is now here.
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7.12.01 As already announced by email, during the week 9-13 December there will be NO TIRGULIM. Instead, all four lecturers will give an EXTRA ONE HOUR LECTURE at the time of the tirgul. So altogether each group will have THREE HOURS of lectures this week. (The reason of course is to reduce the gap between lectures and tirgulim caused by the strike.)

Sunday 9 December:
Prof. Michael Cwikel 9:30-10:30 ULMANN 307.

Dr. Yakov Lutsky 14:30-15:30 ULMANN 310.

Wednesday 12 December:
Dr. Alla Shmukler 9:30-10:30 CHURCHILL AUDITORIUM ("sofi").

Dr. Benzion Kon 14:30-15:30 ULMANN 205 ("sofi").

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29.11.01 You can find some new (updated) notes (4 pages, English) here. These notes explain the topics that we are teaching now or will be teaching soon, (the projection theorem, Bessel's inequality and the Riemann-Lebesgue lemma) in a slightly different way from the text book. Now might be a good time for you to read them.

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The first set of homework exercises (about inner product spaces) is here (Hebrew, 3 pages). But most of these exercises cannot be solved until you learn a few more topics. Some of the harder questions are marked with an asterisk(*).

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We will wait a few days more to publicize our exact policy about bakhanim, tsiyun magen etc. because of possible changes to our original policy because of the strike.

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28.10.01 Last semester's page for Fourier S. I. T. is here. It contains several lists of problems and extra explanations about material from the lectures, and some examinations and solutions to some of them. Most of these things can also be useful this semester. As the semester proceeds I plan to also put more explicit links here to some of these items.